A set is a set which can be expressed as the intersection of a countable collection of open sets.
The complement of a set is an set.
For example, the closed interval is a set because
![$ [-1,+1] \in \mathbb{R}$](http://images.planetmath.org:8080/cache/objects/6216/l2h/img4.png "$ [-1,+1] \in \mathbb{R}$"){kind=small}
![$\displaystyle [-1,+1] = \bigcap_{n=1}^\infty \left( -{1 \over n}-1,{1 \over n}+1 \right)$](http://images.planetmath.org:8080/cache/objects/6216/l2h/img6.png "$\displaystyle [-1,+1] = \bigcap_{n=1}^\infty \left( -{1 \over n}-1,{1 \over n}+1 \right)$")